Question

Joshua borrowed $1,700 on January 1, 2014, and paid $85 in interest. The bank charged him a service charge of $17. He paid it all back at once on December 31, 2014. What was the APR

Answer 1

Given:

Amount borrowed = $1700

Interest = $85

Service charge = $17

To find:

Annual Percentage Rate

Solution:

If the $17 service charge was added to the loan (if Joshua didn't pay the service charge up front), he/she borrowed $1717 and paid $85 as interest for a total of 1802.

$\Rightarrow\text{Annual Percentage Rate}=(\frac{1802}{1717}-1)\times100\rightarrow(1.0495-1)\times100\\\\ \Rightarrow\text{Annual Percentage Rate}=0.0495\times100\rightarrow4.95\%$

But if Joshua indeed paid the $17 up front, then the Annual Percentage Rate will be as follows,

$\Rightarrow\text{Annual Percentage Rate}=(\frac{1785}{1717}-1)\times100\rightarrow(1.0396-1)\times100\\\\ \Rightarrow\text{Annual Percentage Rate}=0.0396\times100\rightarrow3.96\%$

An annual percentage rate (APR) is the annual rate charged for borrowing or earned through an investment.